Significant Digits. l Significant figures are extremely important when reporting a numerical value. l The number of significant figures used indicates.

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Presentation transcript:

Significant Digits

l Significant figures are extremely important when reporting a numerical value. l The number of significant figures used indicates the confidence (certainty) of that value.

Significant Digits l How many? Number known to:Number of sig. figures etc. 1 part per 10 1 part per part per part per etc.

Significant Digits l A significant figure is an accurate digit although the last digit is accepted to have some error. l If length = 7.58 cm l The number of significant figures does not include zeros required to place decimal points. Slight error exact

Significant Digits l Significant digits allow us to systematically express a degree of confidence in a number. l A significant digit or figure is any digit used in a number except: l Zeros that are used to locate the decimal point, such as: l Zeros that do not have any nonzero digits on their left, such as:

Significant Digits l Do the numbers 5000 and imply the same significance? l contains four significant digits. l 5000 is an ambiguous number. It contains either one, two, three, or four significant digits. l How do you write 5000 to two significant digits? l Use scientific notation: 5.0 X 10 3

Significant Digits l How many significant figures should you use? l The number of significant digits used implies a certain maximum error range.

Significant Digits Example: The number 101 has three significant figures and means a number between and The error range is 1 ( 0.5) or about 1% of 101. Three significant figures implies a maximum error range of 1%. Four significant figures implies a maximum error range of 0.1%. Only in exceptional cases will precision better that 0.1% (four significant figures) be necessary in engineering problems.

Rules for Significant Digits l In multiplication and division - use as many significant digits as the number that has the fewest (excluding exact conversion factors) (4.00 kg) (4 m/s 2 ) = 20 kg m/s 2 l In addition and subtraction - line up the decimals and retain the least significant place (Answer)

Rules for Significant Digits Combined operations: If products or quotients are to be added or subtracted, perform the multiplication and division first, establish the correct number of significant figures in the subanswer, perform the addition and subtraction, then round to the proper number of significant figures.